Right now the New York Fed has a permanent seat on the Federal Open Market Committee, an internal monetary policymaking part of the Federal Reserve that will make the decision on when to increase interest rates.

But if GOP lawmakers have their way, the New York Fed's elevated influence will come to an end.

They want to strip the New York central bank branch of its permanent FOMC status and reduce its standing on the committee.

It would not be in the central bank's interest to have William Dudley, president of the New York Fed, excluded from key policy-making decisions because New York City is the East Coast's financial center, a source familiar with the Federal Reserve said. Few feel other central bank presidents would have up-to-the-moment understanding of policy decisions and their ramifications, the source said.

As Business Insider previously reported, lawmakers on the House Financial Services Committee Monetary Policy and Trade Subcommittee this week would hear a proposal that would strip the New York branch of the Federal Reserve of its elevated status on the FOMC. That proposal was, in fact, pitched by one Republican on July 22.

A bill drafted by Michigan Republican committee member Bill Huizenga aims to rotate in and out every Federal Reserve bank branch in alternating years. This means that in odd-numbered years, the Fed banks of Boston, Philadelphia, Richmond, Chicago, Minneapolis, and Dallas would send a representative to the FOMC to make key policy decisions.

In even-numbered years, New York, Cleveland, Atlanta, St. Louis, Kansas City and San Francisco would provide representatives to the FOMC.

The draft also aims to expand the authority of the Government Accountability Office to audit the bank's interest rate policies, something that Yellen and other Fed members have historically opposed. But the latest leak scandal at the Fed could weaken the central bank's defenses before lawmakers the next time she visits Capitol Hill.